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                <h2 id="全排列合集"><a href="#全排列合集" class="headerlink" title="全排列合集"></a>全排列合集</h2><h3 id="leetcode17-电话号码的字母组合"><a href="#leetcode17-电话号码的字母组合" class="headerlink" title="leetcode17-电话号码的字母组合"></a>leetcode17-电话号码的字母组合</h3><p>给定一个仅包含数字 <code>2-9</code> 的字符串，返回所有它能表示的字母组合。答案可以按 <strong>任意顺序</strong> 返回。数字到字母的映射为9键输入法。</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">class</span> <span class="token class-name">Solution</span> <span class="token punctuation">&#123;</span>
    <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">String</span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">HashMap</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Character</span><span class="token punctuation">,</span><span class="token class-name">String</span><span class="token punctuation">></span></span> map<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">String</span><span class="token punctuation">></span></span> <span class="token function">letterCombinations</span><span class="token punctuation">(</span><span class="token class-name">String</span> digits<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>digits<span class="token operator">==</span><span class="token keyword">null</span><span class="token operator">||</span>digits<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">return</span> res<span class="token punctuation">;</span>
        <span class="token comment">//回溯</span>
        map <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">HashMap</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'2'</span><span class="token punctuation">,</span><span class="token string">"abc"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'3'</span><span class="token punctuation">,</span><span class="token string">"def"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'4'</span><span class="token punctuation">,</span><span class="token string">"ghi"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'5'</span><span class="token punctuation">,</span><span class="token string">"jkl"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'6'</span><span class="token punctuation">,</span><span class="token string">"mno"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'7'</span><span class="token punctuation">,</span><span class="token string">"pqrs"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'8'</span><span class="token punctuation">,</span><span class="token string">"tuv"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span><span class="token char">'9'</span><span class="token punctuation">,</span><span class="token string">"wxyz"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token function">dfs</span><span class="token punctuation">(</span>digits<span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token keyword">new</span> <span class="token class-name">StringBuilder</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token class-name">String</span> digits<span class="token punctuation">,</span><span class="token keyword">int</span> index<span class="token punctuation">,</span><span class="token class-name">StringBuilder</span> ans<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>index <span class="token operator">==</span> digits<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>ans<span class="token punctuation">.</span><span class="token function">toString</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>

        <span class="token keyword">char</span><span class="token punctuation">[</span><span class="token punctuation">]</span> ch <span class="token operator">=</span> map<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span>digits<span class="token punctuation">.</span><span class="token function">charAt</span><span class="token punctuation">(</span>index<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">toCharArray</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>ch<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            ans<span class="token punctuation">.</span><span class="token function">append</span><span class="token punctuation">(</span>ch<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token function">dfs</span><span class="token punctuation">(</span>digits<span class="token punctuation">,</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span>ans<span class="token punctuation">)</span><span class="token punctuation">;</span>
            ans<span class="token punctuation">.</span><span class="token function">deleteCharAt</span><span class="token punctuation">(</span>index<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h3 id="hot22-括号生成"><a href="#hot22-括号生成" class="headerlink" title="hot22-括号生成"></a>hot22-括号生成</h3><p>数字n代表生成括号的对数，请你设计一个函数，用于能够生成所有可能的并且有效的括号组合。<br>有效括号组合需满足：左括号必须以正确的顺序闭合。</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> leet22_括号生成 <span class="token punctuation">&#123;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">String</span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">String</span><span class="token punctuation">></span></span> <span class="token function">generateParenthesis</span><span class="token punctuation">(</span><span class="token keyword">int</span> n<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        <span class="token comment">// 全排列</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token function">dfs</span><span class="token punctuation">(</span>n<span class="token punctuation">,</span>n<span class="token punctuation">,</span><span class="token string">""</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> left<span class="token punctuation">,</span><span class="token keyword">int</span> right<span class="token punctuation">,</span><span class="token class-name">String</span> ans<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>left<span class="token operator">==</span><span class="token number">0</span><span class="token operator">&amp;&amp;</span>right<span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>ans<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>

        <span class="token comment">// 如果left>right,最后剩下的都是左括号，直接剪枝</span>
        <span class="token comment">// 一定是先加"("</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>left<span class="token operator">></span>right<span class="token punctuation">)</span> <span class="token keyword">return</span><span class="token punctuation">;</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>left<span class="token operator">></span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token function">dfs</span><span class="token punctuation">(</span>left<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">,</span>right<span class="token punctuation">,</span>ans<span class="token operator">+</span><span class="token string">"("</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>right<span class="token operator">></span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token function">dfs</span><span class="token punctuation">(</span>left<span class="token punctuation">,</span>right<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">,</span>ans<span class="token operator">+</span><span class="token string">")"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<h3 id="剑指38-字符串的排列"><a href="#剑指38-字符串的排列" class="headerlink" title="剑指38-字符串的排列"></a>剑指38-字符串的排列</h3><p>输入一个字符串，打印出该字符串中字符的所有排列。你可以以任意顺序返回这个字符串数组，但里面不能有重复元素。</p>
<p>输入：s &#x3D; “abc”     </p>
<p>输出：[“abc”,”acb”,”bac”,”bca”,”cab”,”cba”]</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">class</span> <span class="token class-name">Solution</span> <span class="token punctuation">&#123;</span>
    <span class="token comment">//hui su</span>
    <span class="token class-name">HashSet</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">String</span><span class="token punctuation">></span></span> hash<span class="token punctuation">;</span>
    <span class="token keyword">boolean</span><span class="token punctuation">[</span><span class="token punctuation">]</span> visited<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">String</span><span class="token punctuation">[</span><span class="token punctuation">]</span> <span class="token function">permutation</span><span class="token punctuation">(</span><span class="token class-name">String</span> s<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>s<span class="token operator">==</span><span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token keyword">null</span><span class="token punctuation">;</span>
        hash <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">HashSet</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">char</span><span class="token punctuation">[</span><span class="token punctuation">]</span> ch <span class="token operator">=</span> s<span class="token punctuation">.</span><span class="token function">toCharArray</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        visited <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token keyword">boolean</span><span class="token punctuation">[</span>ch<span class="token punctuation">.</span>length<span class="token punctuation">]</span><span class="token punctuation">;</span>
		<span class="token function">dfs</span><span class="token punctuation">(</span>ch<span class="token punctuation">,</span><span class="token keyword">new</span> <span class="token class-name">StringBuilder</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token class-name">String</span><span class="token punctuation">[</span><span class="token punctuation">]</span> res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">String</span><span class="token punctuation">[</span>hash<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">;</span>

        <span class="token class-name">Iterator</span> it <span class="token operator">=</span> hash<span class="token punctuation">.</span><span class="token function">iterator</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span> index <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
        <span class="token keyword">while</span><span class="token punctuation">(</span>it<span class="token punctuation">.</span><span class="token function">hasNext</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            res<span class="token punctuation">[</span>index<span class="token operator">++</span><span class="token punctuation">]</span> <span class="token operator">=</span> it<span class="token punctuation">.</span><span class="token function">next</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">toString</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> 
        <span class="token punctuation">&#125;</span>

        <span class="token keyword">return</span> res<span class="token punctuation">;</span>

    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">char</span><span class="token punctuation">[</span><span class="token punctuation">]</span> ch<span class="token punctuation">,</span><span class="token class-name">StringBuilder</span> ans<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>ans<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">==</span>ch<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            hash<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>ans<span class="token punctuation">.</span><span class="token function">toString</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>ch<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
                visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">=</span><span class="token boolean">true</span><span class="token punctuation">;</span>
                ans<span class="token punctuation">.</span><span class="token function">append</span><span class="token punctuation">(</span>ch<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
                <span class="token function">dfs</span><span class="token punctuation">(</span>ch<span class="token punctuation">,</span>ans<span class="token punctuation">)</span><span class="token punctuation">;</span>
                <span class="token comment">//hui su</span>
                ans<span class="token punctuation">.</span><span class="token function">deleteCharAt</span><span class="token punctuation">(</span>ans<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
                visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
            <span class="token punctuation">&#125;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>




<h3 id="leetcode39-组合总和"><a href="#leetcode39-组合总和" class="headerlink" title="leetcode39-组合总和"></a>leetcode39-组合总和</h3><p>给定一个无重复元素的正整数数组 candidates 和一个正整数 target ，找出 candidates 中所有可以使数字和为目标数 target 的唯一组合。candidates 中的数字可以无限制重复被选取。如果至少一个所选数字数量不同，则两种组合是唯一的。</p>
<p>输入: candidates &#x3D; [2,3,6,7], target &#x3D; 7</p>
<p>输出: [[7],[2,2,3]]</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java">
<span class="token keyword">public</span> <span class="token keyword">class</span> leetcode39_组合总和 <span class="token punctuation">&#123;</span>

    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token class-name">String</span><span class="token punctuation">[</span><span class="token punctuation">]</span> args<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums <span class="token operator">=</span> <span class="token punctuation">&#123;</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">6</span><span class="token punctuation">,</span><span class="token number">7</span><span class="token punctuation">&#125;</span><span class="token punctuation">;</span>
        <span class="token class-name">System</span><span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span><span class="token keyword">new</span> leetcode39_组合总和<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">combinationSum</span><span class="token punctuation">(</span>nums<span class="token punctuation">,</span><span class="token number">7</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span></span> path<span class="token punctuation">;</span>

    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> <span class="token function">combinationSum</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> candidates<span class="token punctuation">,</span> <span class="token keyword">int</span> target<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        path <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>candidates<span class="token operator">==</span><span class="token keyword">null</span><span class="token operator">||</span>candidates<span class="token punctuation">.</span>length<span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">return</span> res<span class="token punctuation">;</span>
        <span class="token comment">//回溯</span>
        <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>candidates<span class="token punctuation">,</span>target<span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> depth<span class="token punctuation">,</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">,</span><span class="token keyword">int</span> k<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>k<span class="token operator">&lt;</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token comment">//终止条件</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>k<span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span>path<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> depth<span class="token punctuation">;</span>j<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>j<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            path<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            k <span class="token operator">-=</span> nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
            <span class="token comment">// j从i开始，下一级要不要用j+1，关键在于可不可以重复</span>
            <span class="token comment">//可以重复则下一次还从j开始往后查找</span>
            <span class="token function">dfs</span><span class="token punctuation">(</span>j<span class="token punctuation">,</span>nums<span class="token punctuation">,</span>k<span class="token punctuation">)</span><span class="token punctuation">;</span>

            <span class="token comment">//回溯</span>
            path<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            k<span class="token operator">+=</span> nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<h3 id="leetcode40-组合总和2"><a href="#leetcode40-组合总和2" class="headerlink" title="leetcode40-组合总和2"></a>leetcode40-组合总和2</h3><p>给定一个数组 candidates 和一个目标数 target ，找出 candidates 中所有可以使数字和为 target 的组合。candidates 中的每个数字在每个组合中只能使用一次。</p>
<p>注意：解集不能包含重复的组合。 </p>
<p>39中输入无重复元素，所以每次只向后搜索就没有重复解</p>
<p>40中输入有重复元素，要想办法去重</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> leetcode40_组合总和<span class="token number">2</span> <span class="token punctuation">&#123;</span>

    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token class-name">String</span><span class="token punctuation">[</span><span class="token punctuation">]</span> args<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums <span class="token operator">=</span> <span class="token punctuation">&#123;</span><span class="token number">10</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">7</span><span class="token punctuation">,</span><span class="token number">6</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">&#125;</span><span class="token punctuation">;</span>
        <span class="token class-name">System</span><span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span><span class="token keyword">new</span> leetcode40_组合总和<span class="token function">2</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">combinationSum2</span><span class="token punctuation">(</span>nums<span class="token punctuation">,</span><span class="token number">8</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span></span> path<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> <span class="token function">combinationSum2</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> candidates<span class="token punctuation">,</span> <span class="token keyword">int</span> target<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        path <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>candidates<span class="token operator">==</span><span class="token keyword">null</span><span class="token operator">||</span>candidates<span class="token punctuation">.</span>length<span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">return</span> res<span class="token punctuation">;</span>

        <span class="token comment">//关键问题：去重</span>
        <span class="token comment">//先排序，按顺序搜索答案，这样的结果就可以利用hash去重了</span>
        <span class="token class-name">Arrays</span><span class="token punctuation">.</span><span class="token function">sort</span><span class="token punctuation">(</span>candidates<span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>candidates<span class="token punctuation">,</span>target<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> depth<span class="token punctuation">,</span> <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">,</span><span class="token keyword">int</span> k<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>k<span class="token operator">&lt;</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>k<span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token class-name">ArrayList</span> temp <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span>path<span class="token punctuation">)</span><span class="token punctuation">;</span>
            res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>temp<span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token punctuation">&#125;</span>

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> depth<span class="token punctuation">;</span>j<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>j<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token comment">// 去重,排序之后，j==depth的不用考虑，j>depth后,如果出现重复元素,j==depth里肯定已经考虑过了,剪枝</span>
            <span class="token comment">// 本题与全排列2的区别在于，</span>
            <span class="token comment">// 全排列走到后面时还需要在访问前面的元素，元素个数是全的，所以要通过visited记录是否访问过，</span>
            <span class="token comment">// 而本题排序之后每次就从j往后搜索，不用再考虑j之前的元素了，所以不需要利用visited</span>
            <span class="token comment">// 因此本题无法通过visited判断重复，而是用j>depth判断是否要判断去重</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>j<span class="token operator">></span>depth<span class="token operator">&amp;&amp;</span>nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token operator">==</span>nums<span class="token punctuation">[</span>j<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token keyword">continue</span><span class="token punctuation">;</span>
            
            k <span class="token operator">-=</span> nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
            path<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

            <span class="token comment">// 不能重复使用，下一次递归从下一个开始</span>
            <span class="token comment">// 从j+1继续，表示每一层只搜索j+1之后的</span>
            <span class="token function">dfs</span><span class="token punctuation">(</span>j<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span>nums<span class="token punctuation">,</span>k<span class="token punctuation">)</span><span class="token punctuation">;</span>

            k<span class="token operator">+=</span> nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
            path<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>

<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<h3 id="leetcode46-全排列"><a href="#leetcode46-全排列" class="headerlink" title="leetcode46-全排列"></a>leetcode46-全排列</h3><p>给定一个不含重复数字的数组 nums ，返回其 所有可能的全排列 。你可以 按任意顺序 返回答案。</p>
<p>输入：nums &#x3D; [1,2,3]</p>
<p>输出：[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> leetcode46_全排列 <span class="token punctuation">&#123;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span></span> path<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> <span class="token function">permute</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        path <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token comment">//不可重复访问，用visited标记</span>
        <span class="token keyword">boolean</span><span class="token punctuation">[</span><span class="token punctuation">]</span> visited <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token keyword">boolean</span><span class="token punctuation">[</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">]</span><span class="token punctuation">;</span>
        <span class="token comment">// 从深度depth=0开始向下搜索</span>
        <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>nums<span class="token punctuation">,</span>visited<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> depth<span class="token punctuation">,</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">,</span><span class="token keyword">boolean</span><span class="token punctuation">[</span><span class="token punctuation">]</span> visited<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
        <span class="token comment">//搜索深度到达最底一层</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>depth<span class="token operator">==</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span>path<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
        <span class="token comment">//每一层搜索从数组里找一个还没被访问过的加入路径</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
                visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
                path<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
                <span class="token comment">// 从depth+1继续，每一层都会把所有元素搜索</span>
                <span class="token function">dfs</span><span class="token punctuation">(</span>depth<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span>nums<span class="token punctuation">,</span>visited<span class="token punctuation">)</span><span class="token punctuation">;</span>
                <span class="token comment">// 回溯</span>
                visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
                path<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token punctuation">&#125;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<h3 id="leetcode47-全排列2"><a href="#leetcode47-全排列2" class="headerlink" title="leetcode47-全排列2"></a>leetcode47-全排列2</h3><p>给定一个可包含重复数字的序列 nums ，按任意顺序返回所有不重复的全排列。</p>
<p>输入：nums &#x3D; [1,1,2]</p>
<p>输出：[[1,1,2],[1,2,1],[2,1,1]]</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> leetcode47_全排列<span class="token number">2</span> <span class="token punctuation">&#123;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span></span> path<span class="token punctuation">;</span>

    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> <span class="token function">permuteUnique</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>

        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        path <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token comment">// 利用排序按顺序检索，每层去重</span>
        <span class="token class-name">Arrays</span><span class="token punctuation">.</span><span class="token function">sort</span><span class="token punctuation">(</span>nums<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">boolean</span><span class="token punctuation">[</span><span class="token punctuation">]</span> visited <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token keyword">boolean</span><span class="token punctuation">[</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">]</span><span class="token punctuation">;</span>

        <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>nums<span class="token punctuation">,</span>visited<span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> depth<span class="token punctuation">,</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">,</span><span class="token keyword">boolean</span><span class="token punctuation">[</span><span class="token punctuation">]</span> visited<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>depth<span class="token operator">==</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span>path<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token comment">// 112 和211的区别在于 112走到11时前一个1还在使用中，不是重复的结果，</span>
            <span class="token comment">// 到第二个112时，1开始判断发现前一个1没被使用，即他是被回溯过的，再搜索他会有重复结果出现，剪枝</span>
            <span class="token comment">// 同理第一个211正常，走到第二个211时，发现前一个1刚回溯过，所以剪枝</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>i<span class="token operator">></span><span class="token number">0</span><span class="token operator">&amp;&amp;</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">==</span>nums<span class="token punctuation">[</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">&amp;&amp;</span><span class="token operator">!</span>visited<span class="token punctuation">[</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token keyword">continue</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>

                visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
                path<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

                <span class="token comment">// 从depth+1继续，每一层都会把所有元素搜索</span>
                <span class="token function">dfs</span><span class="token punctuation">(</span>depth<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span>nums<span class="token punctuation">,</span>visited<span class="token punctuation">)</span><span class="token punctuation">;</span>

                path<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
                visited<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
            <span class="token punctuation">&#125;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<h3 id="leetcode78-子集"><a href="#leetcode78-子集" class="headerlink" title="leetcode78-子集"></a>leetcode78-子集</h3><p>给你一个整数数组 nums ，数组中的元素 互不相同 。返回该数组所有可能的子集（幂集）。解集不能包含重复的子集。你可以按任意顺序返回解集。</p>
<p>输入：nums &#x3D; [1,2,3]</p>
<p>输出：[[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> leetcode78_子集 <span class="token punctuation">&#123;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span></span> path<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> <span class="token function">subsets</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        path <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token function">backtrack</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> nums<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> res<span class="token punctuation">;</span>

    <span class="token punctuation">&#125;</span>

    <span class="token keyword">private</span> <span class="token keyword">void</span> <span class="token function">backtrack</span><span class="token punctuation">(</span><span class="token keyword">int</span> depth<span class="token punctuation">,</span> <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        <span class="token comment">// 不用再判断深度有没有达到，记录每一次路径即子集</span>
        res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span>path<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token comment">// j从depth开始搜索，depth之前已经搜索过的就不需要再搜索了，不从0开始，从0开始是重复的</span>
        <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> depth<span class="token punctuation">;</span> j <span class="token operator">&lt;</span> nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>

            path<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token comment">// j+1 表示第j个不能重复使用</span>
            <span class="token function">backtrack</span><span class="token punctuation">(</span>j <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">,</span> nums<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token comment">// 回溯</span>
            path<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<h3 id="leetcode90-子集2"><a href="#leetcode90-子集2" class="headerlink" title="leetcode90-子集2"></a>leetcode90-子集2</h3><p>给你一个整数数组 nums ，其中可能包含重复元素，请你返回该数组所有可能的子集（幂集）。解集 不能 包含重复的子集。返回的解集中，子集可以按 任意顺序排列。</p>
<p>输入：nums &#x3D; [1,2,2]</p>
<p>输出：[[],[1],[1,2],[1,2,2],[2],[2,2]]</p>
<pre class="line-numbers language-java" data-language="java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> leetcode90_子集<span class="token number">2</span> <span class="token punctuation">&#123;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> res<span class="token punctuation">;</span>
    <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span></span> path<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token class-name">List</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token class-name">List</span><span class="token punctuation">&lt;</span><span class="token class-name">Integer</span><span class="token punctuation">></span><span class="token punctuation">></span></span> <span class="token function">subsetsWithDup</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">)</span> <span class="token punctuation">&#123;</span>
        res <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        path <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token comment">// 通过排序后，按顺序深度搜索以去重</span>
        <span class="token class-name">Arrays</span><span class="token punctuation">.</span><span class="token function">sort</span><span class="token punctuation">(</span>nums<span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>nums<span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token keyword">return</span> res<span class="token punctuation">;</span>
    <span class="token punctuation">&#125;</span>

    <span class="token keyword">void</span> <span class="token function">dfs</span><span class="token punctuation">(</span><span class="token keyword">int</span> depth<span class="token punctuation">,</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> nums<span class="token punctuation">)</span><span class="token punctuation">&#123;</span>

        res<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token generics"><span class="token punctuation">&lt;</span><span class="token punctuation">></span></span><span class="token punctuation">(</span>path<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> depth<span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">&#123;</span>
            <span class="token comment">// 判断此时搜索的是不是前面搜索过的重复元素</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>i<span class="token operator">></span>depth<span class="token operator">&amp;&amp;</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">==</span>nums<span class="token punctuation">[</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token keyword">continue</span><span class="token punctuation">;</span>
            path<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

            <span class="token comment">// 从i+1继续，每一层只搜索i+1之后的</span>
            <span class="token function">dfs</span><span class="token punctuation">(</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span>nums<span class="token punctuation">)</span><span class="token punctuation">;</span>

            path<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>path<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token punctuation">&#125;</span>
    <span class="token punctuation">&#125;</span>
<span class="token punctuation">&#125;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>


                
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